def test2_1(self):
print("====test2_1============================")
nn = 100
x = numpy.arange(nn, dtype=float) / 50
ym = 0.2 + 0.5 * x
nf = 0.1
numpy.random.seed(2345)
noise = numpy.random.randn(nn)
y = ym + nf * noise
limits = [-1, 2]
pm = PolynomialModel(1)
bf = Fitter(x, pm)
pars = bf.fit(y)
logz0 = bf.getLogZ(limits=limits)
logl0 = bf.logLikelihood
print("pars ", fmt(pars))
print("stdv ", fmt(bf.stdevs))
print("logZ ", fmt(logz0), " logL ", fmt(logl0))
errdis = GaussErrorDistribution()
problem = ClassicProblem(pm, xdata=x, ydata=y)
logz1, logl1 = plotErrdis2d(errdis,
problem,
limits=limits,
max=0,
plot=self.doplot)
if self.doplot:
plt.plot(pars[0], pars[1], 'k.')
print("logZ ", fmt(logz1), " logL ", fmt(logl1))
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
ns = NestedSampler(x, model, y, verbose=0)
logE = ns.sample()
par2 = ns.parameters
logz2 = ns.logZ
dlz2 = ns.logZprecision
print("pars ", fmt(par2))
print("stdv ", fmt(ns.stdevs))
print("logZ ", fmt(logz2), " +- ", fmt(dlz2))
self.assertTrue(abs(logz2 - logz0) < 1.0)
# print( logz0 - logz1, logz0 - logz2 )
samples = ns.samples
parevo = samples.getParameterEvolution()
llevo = samples.getLogLikelihoodEvolution()
lwevo = samples.getLogWeightEvolution()
assertAAE(numpy.sum(numpy.exp(lwevo)), 1.0)
if self.doplot:
plt.show()
def test7(self):
print("====test7 Poisson ================")
plot = self.doplot
nn = 100
x = numpy.linspace(0, 10, nn, dtype=float)
ym = 1.9 + 2.2 * x
numpy.random.seed(2345)
y = numpy.random.poisson(ym, size=nn)
limits = [0, 4]
if plot:
plt.plot(x, ym, 'k-')
plt.plot(x, y, 'r.')
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
bf = AmoebaFitter(x, model, errdis="poisson")
pars = bf.fit(y, tolerance=1e-20)
print("pars ", fmt(pars))
print("stdv ", fmt(bf.stdevs))
logz0 = bf.getLogZ(limits=limits)
logl0 = bf.logLikelihood
print("logZ ", fmt(logz0), " logl ", fmt(logl0))
errdis = PoissonErrorDistribution()
problem = ClassicProblem(model, xdata=x, ydata=y)
logz1, logl1 = plotErrdis2d(errdis,
problem,
limits=limits,
max=0,
plot=plot)
if plot:
plt.plot(pars[0], pars[1], 'k.')
print("logZ ", fmt(logz1), " logL ", fmt(logl1))
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
ns = NestedSampler(x,
model,
y,
distribution='poisson',
verbose=0,
seed=23456)
logE = ns.sample()
par2 = ns.parameters
logE = ns.logZ
dlz2 = ns.logZprecision
logz2 = ns.logZ
samples = ns.samples
print("pars ", fmt(par2), fmt(samples.maxLikelihoodParameters))
print("stdv ", fmt(ns.stdevs))
print("logZ ", fmt(logz2), " +- ", fmt(dlz2))
self.assertTrue(abs(logz2 - logz1) < 3 * dlz2)
parevo = samples.getParameterEvolution()
llevo = samples.getLogLikelihoodEvolution()
lwevo = samples.getLogWeightEvolution()
assertAAE(numpy.sum(numpy.exp(lwevo)), 1.0)
if plot:
plt.plot(parevo[:, 0], parevo[:, 1], 'k,')
plt.show()
def test6(self):
print("====test6 Laplace ================")
plot = self.doplot
nn = 20
x = numpy.linspace(0, 2, nn, dtype=float)
ym = 0.3 + 0.5 * x
nf = 0.9
numpy.random.seed(12345)
noise = numpy.random.laplace(size=nn)
y = ym + nf * noise
limits = [-1, 2]
if plot:
plt.plot(x, ym, 'k-')
plt.plot(x, y, 'r.')
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
bf = AmoebaFitter(x, model, errdis="laplace")
pars = bf.fit(y, tolerance=1e-20)
print("pars ", fmt(pars))
print("stdv ", fmt(bf.stdevs))
logz0 = bf.getLogZ(limits=limits)
logl0 = bf.logLikelihood
print("logZ ", fmt(logz0), " logL ", fmt(logl0))
errdis = LaplaceErrorDistribution(scale=nf)
problem = ClassicProblem(model, xdata=x, ydata=y)
logz1, logl1 = plotErrdis2d(errdis,
problem,
limits=limits,
max=0,
plot=plot)
if plot:
plt.plot(pars[0], pars[1], 'k.')
print("logZ ", fmt(logz1), " logL ", fmt(logl1))
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
ns = NestedSampler(x,
model,
y,
distribution='laplace',
seed=8945,
verbose=0,
rate=0.5)
logE = ns.sample()
par2 = ns.parameters
logE = ns.logZ
dlz2 = ns.logZprecision
logz2 = ns.logZ
print("pars ", fmt(par2))
print("stdv ", fmt(ns.stdevs))
print("logZ ", fmt(logz2), " +- ", fmt(dlz2))
self.assertTrue(abs(logz2 - logz1) < 4 * dlz2)
# print( logz0 - logz1, logz0 - logz2 )
samples = ns.samples
parevo = samples.getParameterEvolution()
llevo = samples.getLogLikelihoodEvolution()
lwevo = samples.getLogWeightEvolution()
assertAAE(numpy.sum(numpy.exp(lwevo)), 1.0)
if plot:
plt.plot(parevo[:, 0], parevo[:, 1], 'k,')
plt.show()
def test4(self):
print("====test4===unknown noisescale=========================")
plot = self.doplot
nn = 100
x = numpy.arange(nn, dtype=float) / 50
ym = 0.4 + 0.0 * x
nf = 0.5
numpy.random.seed(2345)
noise = numpy.random.randn(nn)
y = ym + nf * noise
limits = [0, 1]
nslim = [0.1, 1.0]
pm = PolynomialModel(0)
bf = Fitter(x, pm)
pars = bf.fit(y)
scale = bf.scale
logz0 = bf.getLogZ(limits=limits, noiseLimits=nslim)
logl0 = bf.logLikelihood
print("pars ", fmt(pars), " scale ", fmt(scale))
print("stdv ", fmt(bf.stdevs))
print("logZ ", fmt(logz0), " logL ", fmt(logl0))
if plot:
plt.figure("model")
plotFit(x, data=y, model=pm, ftr=bf, truth=ym, show=False)
errdis = GaussErrorDistribution()
problem = ClassicProblem(pm, xdata=x, ydata=y)
logz1, logl1 = plotErrdis2d(errdis,
problem,
limits=limits,
nslim=nslim,
plot=plot)
if plot:
plt.plot(pars[0], scale, 'k.')
print("logZ ", fmt(logz1), " logL ", fmt(logl1))
model = PolynomialModel(0)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
dis = GaussErrorDistribution()
dis.setLimits(nslim)
ns = NestedSampler(x, model, y, distribution=dis, verbose=0)
logE = ns.sample()
par2 = ns.parameters
scl2 = ns.scale
logz2 = ns.logZ
dlz2 = ns.logZprecision
print("pars ", fmt(par2), " scale ", fmt(scl2))
print("stdv ", fmt(ns.stdevs))
print("logZ ", fmt(logz2), " +- ", fmt(dlz2))
self.assertTrue(abs(logz2 - logz1) < 2 * dlz2)
samples = ns.samples
parevo = samples.getParameterEvolution()
scevo = samples.getScaleEvolution()
llevo = samples.getLogLikelihoodEvolution()
lwevo = samples.getLogWeightEvolution()
assertAAE(numpy.sum(numpy.exp(lwevo)), 1.0)
if plot:
plt.plot(parevo[:, 0], scevo, 'k,')
plt.figure("model") # grab again
yfit = ns.yfit
err = samples.monteCarloError(x)
plt.plot(x, yfit + err, 'b-')
plt.plot(x, yfit - err, 'b-')
plt.show()
def test3(self):
print("====test3======fixed noisescale======================")
plot = self.doplot
nn = 10
x = numpy.linspace(0, 2, nn, dtype=float)
ym = 0.3 + 0.5 * x
nf = 0.2
numpy.random.seed(2345)
noise = numpy.random.randn(nn)
y = ym + nf * noise
limits = [-1, 2]
pm = PolynomialModel(1)
bf = Fitter(x, pm, fixedScale=nf)
pars = bf.fit(y)
logz0 = bf.getLogZ(limits=limits)
logl0 = bf.logLikelihood
print("pars ", fmt(pars))
print("stdv ", fmt(bf.stdevs))
print("logZ ", fmt(logz0), " logL ", fmt(logl0))
if plot:
plt.figure("model")
plotFit(x, data=y, model=pm, ftr=bf, truth=ym, show=False)
errdis = GaussErrorDistribution(scale=nf)
problem = ClassicProblem(pm, xdata=x, ydata=y)
logz1, logl1 = plotErrdis2d(errdis,
problem,
limits=limits,
max=0,
plot=plot)
if plot:
plt.plot(pars[0], pars[1], 'k.')
print("logZ ", fmt(logz1), " logL ", fmt(logl1))
model = PolynomialModel(1)
model.setLimits(lowLimits=limits[0], highLimits=limits[1])
dis = GaussErrorDistribution(scale=nf)
ns = NestedSampler(x,
model,
y,
distribution=dis,
verbose=0,
seed=34512)
logE = ns.sample()
par2 = ns.parameters
logz2 = ns.logZ
dlz2 = ns.logZprecision
print("pars ", fmt(par2))
print("stdv ", fmt(ns.stdevs))
print("logZ ", fmt(logz2), " +- ", fmt(dlz2))
# print( logz0 - logz1, logz0 - logz2 )
self.assertTrue(abs(logz2 - logz0) < 2 * dlz2)
samples = ns.samples
parevo = samples.getParameterEvolution()
llevo = samples.getLogLikelihoodEvolution()
lwevo = samples.getLogWeightEvolution()
assertAAE(numpy.sum(numpy.exp(lwevo)), 1.0)
if plot:
plt.plot(parevo[:, 0], parevo[:, 1], 'k,')
plt.figure("model") # grab again
yfit = ns.modelfit
err = samples.monteCarloError(x)
plt.plot(x, yfit + err, 'b-')
plt.plot(x, yfit - err, 'b-')
plt.show()